Advanced Burstprop: an online energy-efficient local learning paradigm for deep spiking neural networks

Backpropagation through time with surrogate gradients (SG-BPTT) is the state of the art for training deep spiking neural networks (SNNs), but it is offline, with an unrolled graph costing $O(T)$ activation memory, and its backward phase executes dense multiply-accumulate operations. Recent online local learning rules (E-prop, OSTL, OTTT, DECOLLE, ETLP) remove the unrolled graph, yet their weight updates remain dense floating-point multiply-accumulates at every timestep (or, for the event-triggered ETLP, at every triggered timestep), so the backward phase remains the energy sink. This raises a critical question for the field: if training an SNN costs orders of magnitude more energy than its forward pass could ever save, in what sense is the SNN energy-efficient at all? We answer this question with Advanced Burstprop (ABP), an online local learning rule whose backward phase is as event-driven as the forward phase: signed ternary burst events $\{-1,0,+1\}$, emitted at a $\sim 5\%$ rate, carry error transport and weight updates strictly in $O(1)$ memory, multiply-free and accumulate-only. On DVS-Gesture, under the 45 nm CMOS energy model, ABP matches the dense-backward baselines ($90.23\pm 0.78\%$ vs. $92.45\pm 0.60\%$ for the strongest baseline) at $\sim 31\times$ lower backward energy, and the deterministic variant pushes the reduction to $\sim 53\times$. Widening the burst alphabet beyond ternary to $\{-L,\dots ,+L\}$ multiplies the backward energy without accuracy gain, confirming ternary as the optimal code. In a controlled depth sweep, ABP's accuracy decays with depth, but widening the layers, rather than raising the burst rate, recovers it while maintaining the energy-efficiency advantage. On SHD, ABP attains the smallest gap to SG-BPTT among online methods on the temporal-convolutional LSTM architecture while being $\sim 25\times$ more backward-energy-efficient. We further discuss the feasibility of deploying ABP on existing neuromorphic hardware, including Intel Loihi 2 and SpiNNaker 2. To our knowledge, ABP is the first online learning rule to scale multiply-free, event-sparse burst learning to deep SNN architectures, and the first to quantify the resulting energy advantage, making SNN training, not merely SNN inference, energy-efficient.